Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x-y &= -6 \\ -4x-5y &= -3\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-4x = 5y-3$ Divide both sides by $-4$ to isolate $x$ $x = {-\dfrac{5}{4}y + \dfrac{3}{4}}$ Substitute this expression for $x$ in the first equation. $4({-\dfrac{5}{4}y + \dfrac{3}{4}}) - y = -6$ $-5y + 3 - y = -6$ Simplify by combining terms, then solve for $y$ $-6y + 3 = -6$ $-6y = -9$ $y = \dfrac{3}{2}$ Substitute $\dfrac{3}{2}$ for $y$ in the top equation. $4x- \dfrac{3}{2} = -6$ $4x-\dfrac{3}{2} = -6$ $4x = -\dfrac{9}{2}$ $x = -\dfrac{9}{8}$ The solution is $\enspace x = -\dfrac{9}{8}, \enspace y = \dfrac{3}{2}$.